Answer:
The answer is below
Step-by-step explanation:
The question is not complete, what are the coordinates of point Q and R. But I would show how to solve this.
The location of a point O(x, y) which divides line segment AB in the ratio a:b with point A at (
) and B(
) is given by the formula:
If point Q is at () and S at () and R(x, y) divides QS in the ratio QR to RS is 3:5, The coordinates of R is:
Let us assume Q(−9,4) and S(7,−4)
Answer: A. A(1) = 14; A(n) = (n − 1) −4; A(n) = 14 + (n − 1)(−4)
Step-by-step explanation:
Arithmetic sequence is a sequence that is identified by their common difference. Let a be the first term, n be the number of terms and d be the common difference.
For an arithmetic sequence, common difference 'd' is added to the preceding term to get its succeeding term. For example if a is the first term of a sequence, second term will be a+d, third term will give a+d+d and so on to generate sequence of the form,
a, a+d, a+3d, a+4d...
Notice that each new term keep increasing by a common difference 'd'
The nth term of the sequence Tn will therefore give Tn = a+(n-1)d
If the initial (first) term is 14 and common difference is -4, the nth of the sequence will be gotten by substituting a = 14 and d = -4 in the general formula to give;
Tn = 14+(n-1)-4 (which gives the required answer)
Tn = 14-4n+4
Tn = 18-4n
Given:
Joanna :
works 14 hrs a week more than her line workers.
gets paid 6.50 more per hour than her line workers.
Line workers: h = hours per week ; d = dollars per hour.
Line worker = Dollar per hour * number of hours.
Joanna = (Dollar per hour + 6.50)(number of hours + 14 hours)
Line worker:
$576 = d * 36 hours
$576/36 = d
$16 = d hourly rate of line worker.
Joanna:
$16 + 6.50 = $22.50 hourly rate
36hrs + 14hrs = 50 hours per week.
Weekly pay of Joanna: $22.50 * 50 = $1,125
B
Here, x is the volume of the 10ml solution. Multiplying it by its concentration gives the amount of alcohol in it. 50 is the total volume of the 12% solution so (50 - x) gives the volume of the 15% solution. Multiplying this by the concentration gives the amount of alcohol in it. The sum of these amounts of alcohols is equivalent to the amount of alcohol in the 12% solution which is given by the product of its volume and concentration.
Answer:
a. 12
b. 7.200 and 2.683
Step-by-step explanation:
The computation is shown below:
Given that
P = 0.40 and n = 30
a)
The expected value of received e-mails is
= n × p
= 30 × 0.4
= 12
b)
The variance of emails received is
= n × p × (1 - p)
= 30 × 0.4 × 0.6
= 7.200
Now
The standard deviation of emails received is
= sqrt(variance)
= 2.683
We simply applied the above formula
